Ram pressure

Ram pressure is a pressure exerted on a body moving through a fluid medium, caused by relative bulk motion of the fluid rather than random thermal motion. It causes a drag force to be exerted on the body. Ram pressure is given in tensor form as

P ram = ρ u i u j {\displaystyle P_{\text{ram}}=\rho u_{i}u_{j}} , where ρ {\displaystyle \rho } is the density of the fluid; P ram {\displaystyle P_{\text{ram}}} is the momentum flux per second in the i {\displaystyle i} direction through a surface with normal in the j {\displaystyle j} direction. u i , u j {\displaystyle u_{i},u_{j}} are the components of the fluid velocity in these directions. The total Cauchy stress tensor σ i j {\displaystyle \sigma _{ij}} is the sum of this ram pressure and the isotropic thermal pressure (in the absence of viscosity). In the simple case when the relative velocity is normal to the surface, and momentum is fully transferred to the object, the ram pressure becomes

P ram = 1 / 2 ρ u 2 {\displaystyle P_{\text{ram}}=1/2\rho u^{2}} .

Derivation

The Eulerian form of the Cauchy momentum equation for a fluid is

ρ ∂ u → ∂ t = − ∇ → p − ρ ( u → ⋅ ∇ → ) u → + ρ g → {\displaystyle \rho {\frac {\partial {\vec {u}}}{\partial t}}=-{\vec {\nabla }}p-\rho ({\vec {u}}\cdot {\vec {\nabla }}){\vec {u}}+\rho {\vec {g}}}

for isotropic pressure p {\displaystyle p} , where u → {\displaystyle {\vec {u}}} is fluid velocity, ρ {\displaystyle \rho } the fluid density, and g → {\displaystyle {\vec {g}}} the gravitational acceleration. The Eulerian rate of change of momentum in direction i {\displaystyle i} at a point is thus (using Einstein notation):

… excerpt ends here. Continue reading the full article.